Merging and splitting different patches allows one to perform logical entangling gates and multi-qubit Pauli measurements.
Merging (splitting) is achieved by changing the measurement pattern from \(q\)  to \(p\)  (\(p\)  to \(q\) ) in the gap between patches, as illustrated in Fig:patchmerging.
As in the case of deformation, error correction must be performed after the merging for a fault-tolerant implementation For the case of patch merging, it is sometimes useful to introduce twist defects in the process [1]}, [2]}.
This allows for the measurement of a multi-qubit logical Pauli operator involving a logical \(Y\) , alleviating the cost of distilling the eigenstates of the Pauli-\(Y\)  operator \(\vert y \rangle \)  to implement logical \(P\)  gates with the surface code [3]}, [4]}..
